The cumulation of a sum of N observations from a distribution of Y where N and Y are linearly related random variables may serve as a model for the description of sales, insurance payments, changes in stock prices and other economic processes. The expectation and variance of such a sum and other results are presented with an empirical example. This model may prove useful for description of various flow magnitudes per interval of time that are, in turn, random cumulations of random outcomes.
Get full access to this article
View all access options for this article.
References
1.
BarnettH. A. R., “The Variance of the Product of Two Independent Variables and Its Application to an Investigation Based on Sample Data,”Journal of Institute Actuaries, 81 (February 1955), 190.
2.
BenishayHaskel, “A Disaggregative Model for the Generation of Sales,”Journal of Marketing Research, 2 (February 1965), 74–80.
3.
FellerWilliam, An Introduction to Probability Theory and Its Applications, Vol. I. New York: John Wiley & Sons, Inc., 1958, 268, 276.
4.
LeoA. Goodman, “On the Exact Variance of Products,”Journal of the American Statistical Association, 55 (December 1960), 708–13.
5.
LeoA. Goodman, “The Variance of the Product of K Random Variables,”Journal of the American Statistical Association, 57 (March 1962), 54–60.
6.
ShellardG. D., “Estimating the Product of Several Random Variables,”Journal of the American Statistical Association, 47 (June 1952), 216–21.
7.
Simulmatics Media-Mix: Technical Description, New York: The Simulmatics Corporation, October 1962.
8.
YatesF., Sampling Methods for Censuses and Surveys, 2nd ed., London: Charles Griffin and Co., Ltd., 1953.
9.
YuleG. U., and KendallM. G., An Introduction to the Theory of Statistics, 14th ed., New York: Hafner Publishing Co., 1950, 151–68, 199–236.
